An efficient k-means clustering algorithms: Analysis and implementation

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 24; no. 7; pp. 881 - 892
• Main Authors: Kanungo, Tapas, Mount, David M, Netanyahu, Nathan S, Piatko, Christine D, Silverman, Ruth, Wu, Angela Y
• Format: Journal Article
• Language: English
• Published: 01.07.2002
• ISSN: 0162-8828
• DOI: 10.1109/TPAMI.2002.1017616

In k-means clustering, we are given a set of n data points in d-dimensional space R super(d) and an integer k and the problem is to determine a set of k points in R super(d), called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k-means clustering is Lloyd's algorithm. In this paper, we present a simple and efficient implementation of Lloyd's k-means clustering algorithm, which we call the filtering algorithm. This algorithm is easy to implement, requiring a kd-tree as the only major data structure. We establish the practical efficiency of the filtering algorithm in two ways. First, we present a data-sensitive analysis of the algorithm's running time, which allows that the algorithm runs faster as the separation between clusters increases. Second, we present a number of empirical studies both on synthetically generated data and on real data sets from applications in color quantization, data compression, and image segmentation.